Projective dimension in UFDs (Q1577505)

A submodule \(M\) of a module \(N\) over a domain \(R\) is said to be a 0-submodule if \(N/M\) is torsion free. In the paper, a characterization of factorial Noetherian domains in terms of 0-submodules is presented and it is applied to give a criterion for the ring of a hypersurface to be factorial and to reduce a conjecture of Evans and Griffith in syzygies to ideals.